Real-time modeling of heat distributions

ABSTRACT

Techniques for real-time modeling temperature distributions based on streaming sensor data are provided. In one aspect, a method for creating a three-dimensional temperature distribution model for a room having a floor and a ceiling is provided. The method includes the following steps. A ceiling temperature distribution in the room is determined. A floor temperature distribution in the room is determined. An interpolation between the ceiling temperature distribution and the floor temperature distribution is used to obtain the three-dimensional temperature distribution model for the room.

STATEMENT OF GOVERNMENT RIGHTS

This invention was made with Government support under Contract numberDE-EE00002897 awarded by Department of Energy. The Government hascertain rights in this invention.

FIELD OF THE INVENTION

The present invention relates to modeling temperature distributions inan indoor environment, such as a data center, and more particularly, totechniques for real-time modeling temperature distributions based onstreaming sensor data.

BACKGROUND OF THE INVENTION

The energy consumption of data centers has dramatically increased inrecent years, primarily because of the massive computing demands drivenessentially by every sector of the economy, ranging from acceleratingonline sales in the retail business to banking services in the financialindustry. A study estimated the total U.S. DC energy consumption in theyear 2005 to be approximately 1.2% of the total U.S. consumption (up by15% from the year 2000). See, for example, “EPA Report to Congress onServer and Data Center Energy Efficiency” Public Law 109-431, UnitedStates Code, Aug. 2, 2007.

In order to improve data center energy efficiency, it is important to beable to accurately assess the temperature distributions with the datacenter. That way cooling systems can be effectively implemented withgreater efficiency. Further, changing conditions within the data centermake it desirable to be able to determine the temperature distributionsin a timely manner, in order to continually maintain an efficientcooling operation within the data center.

Thus, techniques for real-time modeling temperature distributions wouldbe desirable.

SUMMARY OF THE INVENTION

The present invention provides techniques for real-time modelingtemperature distributions based on streaming sensor data. In one aspectof the invention, a method for creating a three-dimensional temperaturedistribution model for a room having a floor and a ceiling is provided.The method includes the following steps. A ceiling temperaturedistribution in the room is determined. A floor temperature distributionin the room is determined. An interpolation between the ceilingtemperature distribution and the floor temperature distribution is usedto obtain the three-dimensional temperature distribution model for theroom.

A more complete understanding of the present invention, as well asfurther features and advantages of the present invention, will beobtained by reference to the following detailed description anddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating an exemplary data center according toan embodiment of the present invention;

FIG. 2 is a graph illustrating differences of exhaust and inlettemperatures according to an embodiment of the present invention;

FIG. 3 is a diagram illustrating an exemplary methodology for real-timemodeling of heat distributions in an indoor space, such as a datacenter, according to an embodiment of the present invention;

FIG. 4 is a diagram illustrating an exemplary plenum convolution maskaccording to an embodiment of the present invention;

FIG. 5 is a diagram illustrating an exemplary raised floor (RF)convolution mask according to an embodiment of the present invention;

FIG. 6 is a diagram illustrating an exemplary ceiling convolution maskaccording to an embodiment of the present invention;

FIG. 7 is a diagram illustrating an exemplary equipment index accordingto an embodiment of the present invention;

FIG. 8 is a diagram illustrating an exemplary configuration of a datacenter showing a location of inlet thermal sensors and virtual sensorsaccording to an embodiment of the present invention;

FIG. 9 is a diagram illustrating an exemplary sensor table according toan embodiment of the present invention;

FIG. 10 is a diagram illustrating an exemplary plenum temperature arrayaccording to an embodiment of the present invention;

FIG. 11A is a diagram illustrating an exemplary ceiling temperaturearray with a damping constant of 4 according to an embodiment of thepresent invention;

FIG. 11B is a diagram illustrating an exemplary ceiling temperaturearray with a damping constant of 0.1 according to an embodiment of thepresent invention;

FIG. 12 is a diagram illustrating an exemplary plenum pressure arrayaccording to an embodiment of the present invention;

FIG. 13 is a diagram illustrating the flow rate of air in cubic feet perminute (cfm) coming out of each tile according to an embodiment of thepresent invention;

FIG. 14 is a diagram illustrating an exemplary response function matrixaccording to an embodiment of the present invention;

FIG. 15A is a diagram illustrating an exemplary matrix of

$\prod\limits_{q}^{\#\mspace{14mu}{oftiles}}{{resp}^{q}\left( {x,y} \right)}$with w=10 (1.67 feet) according to an embodiment of the presentinvention;

FIG. 15B is a diagram illustrating exemplary matrix of

$\prod\limits_{q}^{\#\mspace{14mu}{oftiles}}{{resp}^{q}\left( {x,y} \right)}$with w=5 (0.83 feet) according to an embodiment of the presentinvention;

FIG. 16A is a diagram illustrating an exemplary floor temperaturedistribution with w=10 (1.67 feet) according to an embodiment of thepresent invention;

FIG. 16B is a diagram illustrating an exemplary floor temperaturedistribution with w=5 (0.83 feet) according to an embodiment of thepresent invention;

FIG. 17A is a diagram illustrating an exemplary raised floor temperaturedistribution at 4.5 feet with ΔT_(V)=12° C. according to an embodimentof the present invention;

FIG. 17B is a diagram illustrating an exemplary raised floor temperaturedistribution at 4.5 feet with ΔT_(V)=4° C. according to an embodiment ofthe present invention; and

FIG. 18 is a diagram illustrating an exemplary apparatus for creating athree-dimensional temperature distribution model for a room having afloor and a ceiling according to an embodiment of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Provided herein are techniques for real-time modeling temperaturedistributions based on streaming sensor data. Also described herein ishow this method can be benchmarked against “detailed” temperaturemeasurements to improve the model accuracy. It is notable that while thepresent techniques are described in the context of data centertemperature modeling, the fundamental concepts can be applied to anyindoor space, including but not limited to buildings, rooms, residentialand commercial dwellings, etc. in the same manner as described.

Traditionally, computational fluid dynamics (CFD) methods are used tomodel such temperature distributions solving a complex system ofcoupled, partial differential equations (PDEs). Although CFD methodshave been successfully deployed to data centers or buildings they comewith long computation times. In fact, it is not often clear whether the“quality” of the input data required to specify the boundaries of thePDEs warrants such detailed computation. Because of these largecomputation times, some other methods have been explored wheretemperature distributions are simply obtained by “interpolation” fromreal-time sensor data. Such techniques may involve inverse distanceinterpolation, kriging methods and/or proper orthogonal decomposition.Although such techniques are much faster than CFD methods they lack thephysical insights and accuracy as well as a way to benchmark and improvetheir accuracy.

In a first aspect of the present techniques a much faster method formodeling temperature distributions is described. FIG. 1 is a diagramillustrating exemplary data center 100. Data center 100 has informationtechnology (IT) racks 101 and a raised-floor cooling system with airconditioning units (ACUs) 102 (also referred to herein as computer roomair conditioners (CRACs), see below) that take hot air in (typicallyfrom above through one or more air returns in the CRACs) and exhaustcooled air into a sub-floor plenum below. The sub-floor plenum may alsobe referred to herein simply as the “plenum.” Hot air flow through datacenter 100 is indicated by light arrows 110 and cooled air flow throughdata center 100 is indicated by dark arrows 112.

In FIG. 1, IT racks 101 use front-to-back cooling and are located onraised-floor 106 with sub-floor 104 beneath. Namely, according to thisscheme, cooled air is drawn in through a front (inlet) side of each rackand warm air is exhausted out from a rear (outlet) side of each rack.The cooled air drawn into the front of the rack is supplied to airinlets of each IT equipment component (servers for example) therein.Space between raised floor 106 and sub-floor 104 defines the sub-floorplenum 108. The sub-floor plenum 108 serves as a conduit to transport,e.g., cooled air from the ACUs 102 to the racks. In a properly-organizeddata center (such as data center 100), racks 101 are arranged in a hotaisle—cold aisle configuration, i.e., having air inlets and exhaustoutlets in alternating directions. Namely, cooled air is blown throughperforated floor tiles 114 in raised-floor 106, from the sub-floorplenum 108 into the cold aisles. The cooled air is then drawn into racks101, via the air inlets, on an air inlet side of the racks and dumped,via the exhaust outlets, on an exhaust outlet side of the racks and intothe hot aisles.

The ACUs typically receive chilled water from a refrigeration chillerplant (not shown), also referred to herein simply as a “chiller.” EachACU typically includes a blower motor to circulate air through the ACUand to blow cooled air, e.g., into the sub-floor plenum. As such, inmost data centers, the ACUs are simple heat exchangers mainly consumingpower needed to blow the cooled air into the sub-floor plenum. Coolantdistribution units (CDUs) (not shown) can be employed at the interfacebetween the chiller and the ACUs. In general, a CDU includes a heatexchanger and one or more circulating pumps to circulate the chilledwater through the ACUs. Thus, as will be described in detail below, theCDUs contribute to the overall power consumption in the data center.

Typically, one or more power distribution units (PDUs) (not shown) arepresent that distribute power to the IT equipment racks 101. As will bedescribed in detail below, power consumption by the PDUs can be animportant consideration in the present techniques. In general, since thePDUs supply electrical power required by the IT equipment in a datacenter, a total electrical power intake of the PDUs represents animportant parameter in determining the energy efficiency of a datacenter. According to an exemplary embodiment, each of the PDUs isoutfitted with commercially available power and current sensors whichmeasure the electric power drawn by each of the PDUs.

Uninterruptable power supplies or UPS (not shown) are also typicallyimplemented in a data center to protect the IT equipment in the event ofa power disruption so as to prevent data loss (i.e., UPS provides shortterm power when the power source fails). As is known in the art, theUPSs might also correct common utility power issues, such as voltagespikes.

The pressure differential between the “pressurized” sub-floor plenum andthe raised floor is measured with a pressure sensor(s) (see sensorlabeled “pressure sensor” in FIG. 1). According to an exemplaryembodiment, multiple pressure sensors are employed throughout theplenum. The cold air delivered from the ACUs through the sub-floorplenum cools the servers. Thermal temperature sensors at the inlet (Tin)of the servers monitor the inlet temperatures of the servers in theracks, and in this example are measured using inlet thermal sensors (seesensors labeled “thermal sensors (inlet)” in FIG. 1, which are presentat the air inlet sides of the racks). The heated air from the exhaust ofthe server is then returned to the ACUs, where it is cooled anddischarged into the sub-floor plenum. The return (or intake) temperature(TR) to the ACUs, discharge temperature (TD) as well as the air flow ofeach ACU are monitored. In the example shown in FIG. 1, the returntemperature (RT) is measured using inlet thermal sensors, the dischargetemperature of each of the ACUs is measured using a discharge thermalsensor (labeled “thermal sensor (discharge)”) and the air flow of eachof the ACUs is measured using a flow sensor (labeled “flow sensor”). Inthe example shown in FIG. 1, the electric power drawn by the racks ismeasured using power and current sensors (labeled “power/currentsensor”) located at each of the racks. Temperature in the plenum ismeasured using a plenum thermal sensor (labeled “plenum thermalsensor”). The use of a plenum thermal sensor(s) is optional, sincereadings of the plenum temperature may be obtained from the thermalsensors (discharge) (see FIG. 1). When equipped with both plenum thermalsensors and thermal sensors (discharge), then the plenum temperature maybe determined based on a composite of the readings from all of thesethermal sensors. Thermal, air flow, pressure, and power/current sensorsare commercially available. These sensors can provide measurement datain real time, which as described below is used in the present modelingtechniques.

As is apparent from the description of FIG. 1, a data center isessentially a room (i.e., an indoor environment) having a ceiling and afloor. In the case of exemplary data center 100 which employsraised-floor cooling, a sub-floor plenum is present beneath the floor.Thus in that case, the floor may also be referred to herein as a raisedfloor (RF). As will be described in detail below, in the present processa modeled ceiling temperature distribution in the data center and amodeled floor temperature distribution are used to determine/model athree-dimensional temperature distribution in the data center (using,e.g., an interpolation process). When reference is made herein to aceiling temperature distribution it is intended to mean the temperaturedistribution in a portion of the data center proximate to the ceiling(i.e., rather than the temperature of the ceiling itself). Thus, forinstance, the ceiling temperature distribution represents a modeling oftemperatures within one foot of the data center ceiling. Similarly, whenreference is made herein to a floor (or raised floor (RF)) temperaturedistribution it is intended to mean the temperature distribution in aportion of the data center proximate to the floor (i.e., rather than thetemperature of the floor itself). Thus, for instance, the floortemperature distribution represents a modeling of temperatures withinone foot of the data center floor. As described in detail below, aplenum temperature distribution is also modeled. This distributionrepresents the temperatures within the sub-floor plenum.

In contrast to other techniques, in the present techniques theinterpolation solution is bound to obey energy balance. The steps of thepresent techniques will be described in detail in conjunction with thedescription of FIG. 3, below. In overview, however, the presenttechniques serve to first obtain a plenum temperature distribution(calculated by two-dimensional (2D) inverse distance interpolation fromreal-time thermal data of sensors in the plenum (here discharge thermalsensors)). It is noted that alternatively 2D CFD calculations couldinstead be used to obtain such plenum temperature distributions. Suchtwo-dimensional (2D) CFD calculations are described, for example, inEnergy Efficient Thermal Management of Data Centers 2012, pp 273-334Hendrik F. Hamann, Vanessa Lopez, Data Center Metrology andMeasurement-Based Modeling Methods, the contents of which areincorporated by reference herein. Then, the total power of the datacenter room is estimated and the mean ceiling temperature is calculatedusing the total measured air flow produced by the ACUs. As depicted inFIG. 1 each ACU is being monitored with a flow sensor indicating theamount of air flow.

While so far only the mean ceiling temperature has been determined, amore detailed ceiling temperature distribution is next calculated byleveraging the inlet thermal sensors distributed at one or more of theinlets of each rack. In order to estimate the exhaust temperatures foreach rack, virtual sensors may optionally be placed at the “exhaust”side of the rack opposite to the inlet thermal sensors. With virtualsensors a knowledge base is used to “estimate” the difference betweeninlet and exhaust temperatures—see FIG. 2. FIG. 2 is a graph 200illustrating differences of exhaust and inlet temperatures in degreeCelsius (° C.) at heights from 0.5 feet to 7.5 feet. The difference canbe a function of the height of the sensor in the data center (based, forexample, on the placement of the sensor on the rack) and/or equipmenttype, power consumption, etc.

Using the real and virtual thermal sensors, a 2D inverse distanceinterpolation is then used to calculate the ceiling temperaturedistribution. In order to account for the fact that the differentsensors are at different heights in the data center (based, for example,on the placement of the sensor on the rack) and thus influence theceiling temperature to a greater or lesser extent, each sensor isweighted by its distance to the ceiling. The dependence is accomplishedwith a “damping” factor as described in further detail below. Once theceiling temperature distribution has been estimated, the mean value ofthat distribution is adjusted so that it obeys the principle of energybalance as previously established.

Next, the floor temperature distribution is estimated. In order to doso, the air flow through each perforated tile is first calculated usingthe tile impedance of each tile and the pressure differential at thetile location. The plenum pressure distribution is obtained by 2Dinverse distance interpolation of the real-time pressure sensors sensingthe pressure differential between the raised floor and the plenum atvarious locations in the data center. In the example shown in FIG. 1,the pressure sensors are located in the plenum. While there might bepressure sensors in locations in the data center other than in theplenum, it is notable that according to the present techniques data fromthe plenum pressure sensors is sufficient. Once, the air flow througheach perforated tile has been calculated, a Lorentzian field is appliedto each tile location. The Lorentzian field is chosen to yield 0 at thecenter of the tile and converge to 1 at large distances from the tile.The width of the Lorentzian field can be a function of the air flowwhere larger flows could result in a slower convergence to 1 withdistance (wider fields, more impact). This process is repeated bymultiplying the Lorentzian fields at each tile location with theprevious fields. The process yields a 2D surface with very low values(close to 0) in the vicinity of tiles and higher values (close to 1) atlocations far away from the tiles. An average temperature increasedistribution in the data center is then calculated, which is given bythe difference between ceiling and plenum temperature distributions.This average temperature increase distribution is multiplied by theproduct of the Lorentzian fields and the plenum temperature distributionis added to it to yield the floor temperature distribution. The processyields floor temperatures very near to the plenum temperature atlocations close to tiles and average temperatures at locations far awayfrom tiles.

Finally, from the ceiling and floor temperature distributions, a threedimensional temperature distribution for the data center room can beobtained by interpolating between these values using differentapproaches. One approach includes using an s-curve. S-curves aredescribed, for example, in U.S. patent application Ser. No. 12/540,213filed by Hamann et al., entitled “Knowledge-Based Models for DataCenters,” the contents of which are incorporated by reference herein. Inthe instant description, a simple linear interpolation between the floorand the ceiling temperature is employed.

In a second aspect of the present techniques, a method is described forimproving the model described in the first aspect above by usingdetailed temperature distribution measurements from the MMT tool/cart.MMT is a technology for optimizing data center infrastructures forimproved energy and space efficiency which involves a combination ofadvanced metrology techniques for rapid measuring/surveying data centers(see, for example, U.S. Pat. No. 7,366,632, issued to Hamann et al.,entitled “Method and Apparatus for Three-Dimensional Measurements,” thecontents of which are incorporated by reference herein) andphysics-based modeling techniques for optimizing a data center facilitywithin a given thermal envelope for optimum space and most-efficientenergy utilization (see, for example, U.S. Application PublicationNumber 2008/0288193 A1, filed by Claassen et al., entitled “Techniquesfor Analyzing Data Center Energy Utilization Practices,” the contents ofwhich are incorporated by reference herein. The MMT cart data can beused to fit parameters as described immediately below. Basically, thegoal is to optimize/fine-tune the process by finding the parameters (seebelow) that give the best fit to the data obtained from the MMT cart.

The parameters to fit include 1) the width of the Lorentzian fields(which can be a function of the perforated air flow), 2) the temperatureincrease across the rack inlet and exhaust (which can be a function ofthe height in the data center, equipment type, etc.) and 3) a dampingparameter, which determines the weights of the thermal sensors as afunction of height. These parameters can be adjusted to minimize theerror between the interpolated three dimensional temperaturedistribution for the data center room and the detailed temperaturedistribution measurements from the MMT tool/cart.

The present techniques are now described in detail by way of referenceto the description of FIG. 3. FIG. 3 is a diagram of an exemplarymethodology 300 for real-time modeling of heat distributions in anindoor space, such as a data center.

To begin the process, information is gathered about the data center (DC)and the elements (ACUs, PDUs, CDUs, sensors, perforated tiles, etc.)within the data center. See, for example, steps 302-330 which are nowdescribed. According to an exemplary embodiment, in step 302, the areaof the data center floor, i.e., floorArea: A_(DC), is determined. Thedata center floor area can be determined by one of skill in the artgiven the physical dimensions of the data center. For instance, giventhe exemplary data center shown in FIG. 1, if the footprint of the flooris a 15 foot by 20 foot rectangle, then the floor area A_(DC) would be15×20=300 square feet.

Next, in step 304, power consumption data is obtained from the datacenter. According to an exemplary embodiment, the following powerconsumption data is obtained:

-   -   power consumption by the data center lighting (e.g., a light        power consumption factor [1.5 W/feet²]),    -   power consumption by the ACUs (e.g., an ACU overhead factor        (about 10 percent (%)),    -   power consumption by the PDUs (e.g., a PDU overhead factor        (about 10%)),    -   power consumption by the CDUs P_(CDU) (e.g., power removed by        water cooling [kW])    -   miscellaneous power consumption in the data center P_(misc)        (e.g., misc power in data center [kW], i.e., power consumption        in the data center by equipment in the data center which do not        receive power through a PDU—power consumption by equipment in        the data center other than the lighting, ACUs, and CDUs which        all receive power through a PDU). Power consumption information        for each ACU, PDU, CDU, etc. in the data center is generally        provided by the equipment manufacturer and thus can be easily        determined based on the number of units in operation. The same        is true for the data center lighting. Each light bulb/tube has a        power consumption rating. Thus, the overall power consumption by        the lighting in the data center can be easily determined.        Optionally, meters may be employed to measure power consumption        at each ACUs, PDUs, CDU, etc. Some energy monitoring systems        (such as those available from BTi Energy Management, Calgary,        Canada) include remote meter reading and reporting capabilities        that are internet enabled and thus data can be easily compiled        and reported.

In step 306, the following data is obtained regarding the ACUs and PDUs:

-   -   blowerPower: P_(blower) ^(j) blower power for j th blower [kW or        horse power]    -   blowerSetting: θ_(blower) ^(j) blower setting for j th blower    -   flowCapacity: φ_(ACU,0) ^(j) flow capacity at 100% blower        setting for j th blower.        Nominal values (manufacturer specification) for flow capacity        may be taken.    -   measuredFlow: φ_(ACU,M) ^(j) measured flow of j th blower.        Measured flow is flow capacity times the blower setting.    -   power: P_(PDU) ^(i) power for i th PDU.        The blower motor power for each of the ACUs and the power for        each of the PDUs can be determined based on the specifications        given by the equipment manufacturer. The blower motor speed        setting is generally set by the data center operator.

In step 308, real-time data is obtained from each of the sensorsdeployed throughout the data center. As provided above, the sensorsemployed in the data center can include, but are not limited to, inletand discharge thermal sensors, flow sensors, pressure sensors, andpower/current sensors. As will be described in detail below, a weight(i.e., w^(n) weight of n^(th) sensor) may be applied to each sensor toaccount for the fact that different sensors are at different heights inthe data center. Thus, each sensor is weighted by its distance to theceiling.

Air flow rates through the perforated tiles in the raised floor dependon the flow resistance (or flow impedance) of the tiles. Thus, the flowimpedance for each tile is obtained:

-   -   flowImpedance: R_(PERF) ^(q) perforated tile flow impedance of q        th tile [Pa/cfm2].        In most cases, the flow impedance information for a given        brand/configuration of perforated tile is known. Alternatively,        the flow impedance of a perforated tile can be determined based        on the perforation of the tile. For instance, the perforated        tile impedance R_(t) may be given by:

${R_{t} = {\frac{1}{2} \times \frac{\rho}{A_{t}^{2}} \times K}},$where A_(t) is the area of the tile and K is a loss coefficient. Theloss coefficient can be determined by:

${K = {{\frac{1}{o^{2}}\left( {1 + {0.5 \times \left( {1 - o} \right)^{0.75}}} \right)} + \left( {1.414\left( {1 - o} \right)^{0.375}} \right)}},$wherein o is the fractional opening or perforation of the tile. See, forexample, Yogendra Joshi and Pramod Kumar (eds.), “Energy EfficientThermal Management of Data Centers,” 2012, DOI:10.1007/978-1-4419-7124-1, the contents of which are incorporated byreference herein. The perforated tiles in the data center might befitted with dampers which can be adjusted to regulate air flow. Dampersincrease the impedance. Thus, in that case, a very large impedance(e.g., 10 times more impedance) is applied.

As will be described in detail below, a floor temperature distributionin the data center will be determined based on convolution of a plenumtemperature distribution and a perforated tile air flow distribution. Asis known in the art, convolution is an operation performed on twofunctions that results in a third function that is a modified version ofone of the original functions. With convolution, masks (convolutionmasks) are applied to the function that ‘translate’ the function.Convolution masks are commonly used in image filtering to enhance imagequality. The convolution masks typically include a matrix of values orweights, which represents the second function.

Thus, in step 310, plenum, raised floor (RF) and ceiling masks arecreated. The information needed to create the mask is the data centerdimensions and the location/dimensions of all the structures (e.g.,pillars), equipment (e.g., racks), furniture etc. in the data center. Anexemplary plenum mask is shown in FIG. 4, an exemplary raised floor (RF)mask is shown in FIG. 5 and an exemplary ceiling mask is shown in FIG.6. Specifically, in the exemplary plenum mask shown in FIG. 4 the whitearea denotes open space, while the black area denotes portions of theplenum that are blocked off (e.g., see FIG. 4 where area of plenumblocked off by pillars (which support the raised floor) are labeled).Similarly, in the exemplary raised floor mask and ceiling mask shown inFIGS. 5 and 6, respectively, open space is shown in white and areasblocked off, e.g., by equipment such as racks and pillars, are shown inblack.

As described above, optionally, virtual sensors may be employed inaccordance with the present techniques at the “exhaust”/outlet side ofthe rack opposite to the inlet thermal sensors. These sensors will alsobe referred to herein as “virtual (outlet) sensors.” This enables one toestimate the exhaust temperatures for each rack. With virtual sensors aknowledge base can be used to “estimate” the difference between inletand exhaust temperatures. An exemplary virtual sensor framework that maybe implemented in accordance with the present techniques is described,for example, in W. Minker et al. (eds.) “Advanced IntelligentEnvironments,” Springer Dordrecht (2009) (hereinafter “Minker”), thecontents of which are incorporated by reference herein. For example, insection 3.2, FIG. 2 of Minker a virtual sensor framework architecture isshown which includes a knowledge base and a framework controller. Theknowledge base manages information related to the virtual sensors andthe framework controller determines which virtual sensors need to becreated based on data from the knowledge base.

According to the present techniques, in step 312, the placement of thevirtual (outlet) sensors (creating virtual sensor locations) will bebased on the location of the inlet thermal sensors, see above. Namely,it is preferable to create a virtual (outlet) sensor at the exhaust sideof a rack opposite a physical inlet sensor. That way the exhausttemperatures for each rack can be determined. Thus, according to anexemplary embodiment, the first step in creating the virtual (outlet)sensor locations is to create an equipment index. The equipment index isbasically a mapping of all of the equipment (e.g., racks) in the datacenter. See for example FIG. 7 which shows an exemplary equipment index.In the equipment index shown in FIG. 7, the black areas denote areas ofthe data center which have no equipment (i.e., zero equipment index).The number code is used to “tag” the equipment. Next, the locations ofeach of the (physical) inlet thermal sensors are determined. Asdescribed, for example, in conjunction with the description of FIG. 1,above, the inlet thermal sensors may be located at the intake side ofthe racks, at various heights on the racks (see FIG. 1). Using theequipment index and the location of the inlet thermal sensors (at theintake side of the racks), virtual (outlet) sensors can simply becreated at the corresponding exhaust side of the racks (opposite theinlet thermal sensors). Thus, in one exemplary configuration, for eachinlet thermal sensor on a rack in the data center, there is acorresponding virtual (outlet) sensor. See, for example, FIG. 8 which isan exemplary configuration of a data center, where inlet thermal sensorlocations are represented by triangles and virtual (outlet) sensorlocations are represented by squares.

The real-time data collected from the physical sensors (see descriptionof step 308, above) may or may not be consistent with the modeldescription of a sensor. For example, MMT has a data model which hasdata for every sensor like its location, its type and other description.It is possible that someone physically puts in a sensor but forgets toupdate the data model. In the case of inconsistencies, sensor filteringmay be performed. For instance, some sensors may be unbound meaning thata real-time value is obtained for a sensor but a corresponding sensordescription is not found in the data model. For example, it may beunknown what type of sensor it is and where it is located.

Another inconsistency that might occur is when a sensor(s), for whichthere is an entry in the data model, may not transmit a real-time value.By way of example only, this might occur because the sensor may befaulty, someone might have removed it or disconnected its power/battery,a network/IT issue may have occurred. Such sensors are classified as“missing.” A further distinction may be made herein between those“missing” sensors which are permanently missing (i.e., those sensorswhich provide no value at all) and those that are temporarily missing(i.e., sensors which provide data but after a specified time out periodhas ended). These sensors which provide data but after a specified timeout period has ended are also referred to herein as “out of timesensors,” or “timed out” sensors and as indicated immediately above areconsidered temporarily missing.

Yet another inconsistency is with regard to sensors which are out ofrange. This can be caused by “bit errors,” which can yield non-physicalvalues. These “out of range” sensors can be identified by specifying anexpected range, and their values can be removed from consideration.

It is notable that, as described above, power consumption by the PDUscan be determined by monitoring power values from each PDU.Alternatively, current values may be monitored for each of three inputs(I) of a PDU (i.e., three phase units will have three values forcurrent). These current values can then be used to determine the powerconsumption associated with this particular PDU using:P _(PDU) ^(i)=(I ₁ ^(i) +I ₂ ^(i) +I ₃ ^(i))/3·208V·√{square root over(3)}·PF,where PF is the power factor (PF˜0.9).

Taking the above-described sensor inconsistencies into account, thenumber (#) of real-time sensors (RTS) (i.e., sensors for which real-timevalues are present) is specified based on the number of model sensors(MS), the number of unbound sensors (see above) and the number ofmissing sensors (see above) as follows:#RTS=#MS+#unbound−#missing.The model sensors (MS) are those sensors which are specified in themodel. See for example FIG. 8 which, as described above, shows thelocations of physical and virtual sensors in the data center. Modelsensors include only physical sensors. The present process generatesvirtual sensors internally for creating heat maps. Unbound sensors wouldhave no corresponding entry in the data model, whereas missing sensorswould have an entry in the data model but no real-time values. Accordingto an exemplary embodiment, a table can be created of the model sensors,highlighting those sensors which are out of time (temporarily missingsensors, see above) and those which are out of range. As provided above,those sensors which are out of time and out of range are removed fromconsideration. Based on the table created, the number of remainingsensors can be determined. An exemplary sensor table is shown in FIG. 9,which is set up for each of the three types of sensors (thermal sensors,pressure sensors and flow sensors) used in the present example.

Given the data collected from the sensors, in step 314, the mean plenumtemperature T_(p) ^(mean) is calculated. According to an exemplaryembodiment, the mean plenum temperature T_(p) ^(mean) is calculated byfirst using inverse weighted distance (IWD) to determine a plenumtemperature distribution T_(p)(x,y) based on the plenum temperaturesensor readings. The plenum temperature readings can be taken from thethermal sensors (discharge) and/or from the plenum thermal sensors, ifavailable (see description of FIG. 1, above). IWD is a commonly employedtechnique for interpolation using a known scattered set of points (inthis case the plenum temperature data). IWD is used to create adistribution (function of x and y) from discrete values. An exemplaryplenum temperature distribution/array is shown in FIG. 10. A key shownto the right of the distribution in FIG. 10 shows temperature valuesranging from 54.2 degrees Fahrenheit (° F.) to 64.1° F.

The plenum temperature distribution (See FIG. 6) is essentially an array(or grid) of regularly spaced data (temperature) points. The plenum mask(created in step 310, described above) is then applied to the plenumtemperature distribution array. Essentially, the mask tells if a pointin the array/grid is occupied by a structure or equipment (in this casea pillar) or is free (unoccupied). By applying the plenum mask, the meanplenum temperature T_(p) ^(mean) is then calculated. The plenum mask isused to eliminate all points occupied by equipment, etc. beforecalculating the mean temperature. As will be described in detail below,the mean plenum temperature T_(p) ^(mean) will be used to calculate theceiling temperature.

Another factor needed to calculate the ceiling temperature is the heatload in the data center. Thus, in step 316, the heat load in the datacenter (also referred to herein as the raised floor or RF) P_(RF) iscalculated. This heat load P_(RF) calculation takes into account thepower consumption of the PDUs P_(PDU) ^(i), the data center floor areaA_(DC), the blower power P_(blower) ^(j) and blower settings θ_(blower)^(j), miscellaneous power consumption P_(misc) and power consumption bythe CDUs P_(CDU) (all of which were obtained as described above) asfollows:

$P_{RF} = {{\sum\limits_{i = 1}^{\#\mspace{14mu}{ofPDUs}}P_{PDU}^{i}} + {{pdu} \cdot {\sum\limits_{i = 1}^{\#\mspace{14mu}{ofPDUs}}P_{PDU}^{i}}} + {{light} \cdot A_{D\; C}} + {\sum\limits_{j = 1}^{\#\mspace{14mu}{ofACUs}}{P_{blower}^{j} \cdot \vartheta_{blower}^{j\; 3}}} + {{acu} \cdot {\sum\limits_{j = 1}^{\#\mspace{14mu}{ofACUs}}{P_{blower}^{j} \cdot \vartheta_{blower}^{j\; 3}}}} + P_{misc} - P_{CDU}}$

Yet another factor needed to calculate the ceiling temperature is theACU air flow in the data center (i.e., the air flow in the data centerattributable to the ACUs/blowers). Thus, in step 318, the ACU air flowφ_(ACU) ^(total) in the data center is calculated. This ACU air flowφ_(ACU) ^(total) calculation takes into account the flow capacity of theACUs φ_(ACU,0) ^(j) and the blower settings θ_(blower) ^(j) as follows:

$\phi_{ACU}^{total} = {\sum\limits_{j}^{\#{ofACUs}}{\phi_{ACU}^{j} \cdot \vartheta_{blower}^{j}}}$

From the mean plenum temperature T_(p) ^(mean) (calculated in step 314),heat load in the data center P_(RF) (calculated in step 316) and the ACUair flow φ_(ACU) ^(total) in the data center (calculated in step 318),the mean ceiling temperature T_(c) ^(mean) can be calculated in step 320as follows:T _(c) ^(mean)=3140 [cfm·F/kW]·P _(RF)/φ_(ACU) ^(total) +T _(p) ^(mean).

While so far only the mean ceiling temperature has been determined, amore detailed ceiling temperature distribution is next calculated byleveraging the inlet thermal sensors distributed at one or more of theinlets of each rack measured using the physical and virtual sensors. Themean ceiling temperature is calculated based on energy balance and it isimportant to know this number because the methodology aims to preserveenergy balance. The detailed ceiling temperature distribution is“scaled” such that its mean is the same as the calculated mean ceilingtemperature. Specifically, in step 322, a weight of each sensor iscalculated. As described above, in order to account for the fact thatthe different sensors are at different heights in the data center(based, for example, on the placement of the sensor on the rack) andthus influence the ceiling temperature to a greater or lesser extent,each thermal sensor (inlet) and virtual (outlet) sensor is weighted byits distance from the ceiling. The dependence is accomplished with adamping constant k. According to an exemplary embodiment, the weight ofeach sensor n is calculated as follows:w _(RF) ^(n)=exp(−(dz−z _(RF) ^(n))/k),with k being the damping constant. Exemplary ceiling temperaturedistributions are shown in FIGS. 11A and 11B (described below) whichemploy different damping constants.

Based on the inlet thermal sensor readings, IWD is used to calculate aceiling temperature distribution T_(c)(x,y). Sensor weights are used inIWD. In this case the weight is w_rf/distance. IWD was described above.Exemplary ceiling temperature distribution/array are shown in FIGS. 11Aand 11B. The ceiling temperature distribution array in FIG. 11A appliesa damping constant k of 4 and the ceiling temperature distribution arrayin FIG. 11B applies a damping constant k of 0.1. According to anexemplary embodiment, the particular damping constant value isdetermined based on trial and error to give a good fit to the MMT cartdata. A key shown to the right of the distribution in FIG. 11A showstemperature values ranging from 69.1° F. to 91.0° F. A key shown to theright of the distribution in FIG. 11B shows temperature values rangingfrom 65.9° F. to 90.6° F.

The ceiling temperature distribution (see FIG. 11A or 11B) isessentially an array (or grid) of regularly spaced data (temperature)points. The ceiling mask (created in step 310, described above) is thenapplied to the ceiling temperature distribution array. Essentially, themask tells if a point in the array/grid is occupied by a structure orequipment (in this case a pillar) or is free (unoccupied). Once theceiling temperature distribution has been estimated, the mean value ofthat distribution is adjusted (normalized) so that it obeys theprinciple of energy balance as previously established to yield thecorrect (based on energy balance) average ceiling temperature. Theenergy balance here makes sure that the mean temperature rise in thedata center is consistent with the amount of heat dissipated by ITequipment, etc. The mean temperature calculated using sensor values ingeneral will not be equal to the mean temperature calculated usingenergy balance. So the whole temperature distribution calculated usingsensor values is scaled so that its mean is the same as that calculatedusing energy balance.

Next, the floor temperature distribution is determined. In order to doso, the air flow through each perforated tile is first calculated usingthe tile impedance of each tile and the pressure differential at thetile location. According to an exemplary embodiment, in step 324, basedon the plenum pressure sensor readings (obtained, e.g., in step 308, seeabove), IWD is used to calculate the plenum pressure distributionP_(P)(x,y). As provided above, IWD is a standard interpolationtechnique. An exemplary plenum pressure distribution/array is shown inFIG. 12. A key shown to the right of the distribution in FIG. 12 showspressure values ranging from 1.8 Pascal (Pa) to 2.6 Pa.

The plenum pressure distribution (See FIG. 12) is essentially an array(or grid) of regularly spaced data (pressure) points. The plenum mask(created in step 310, described above) is then applied to the plenumpressure distribution array. Essentially, the mask tells if a point inthe array/grid is occupied by a structure or equipment (in this case apillar) or is free (unoccupied).

Next, the plenum pressure P_(p) is used to calculate the perforated airflow from each tile φ_(PERF) ^(q) as follows:φ_(PERF) ^(q)=√{square root over (P _(p)(x _(PERF) ^(q) ,y _(PERF)^(q))/R _(PERF) ^(q))}.Using the perforated air flow from each tile φ_(PERF) ^(q), in step 326,the total perforated tile air flow φ_(PERF) ^(total) can be calculatedas follows:

$\phi_{PERF}^{total} = {\sum\limits_{q}{\phi_{PERF}^{q}.}}$FIG. 13 is a diagram illustrating the flow rate of air in cubic feet perminute (cfm) coming out of each tile. A key shown to the right of thedistribution in FIG. 13 shows air flow values ranging from 122 cfm to146 cfm. Where there is no tile the value is zero.

Next, in step 328, the floor temperature T_(f) is calculated. In orderto calculate the floor temperature T_(f), a normalized Lorentzian field(resp) is applied to each tile location as follows:z ^(q)=√{square root over ((x−x _(PERF) ^(q))²+(y−y _(PERF) ^(q))²)}

${{{resp}^{q}\left( {x,y} \right)} = {{\frac{- 1}{w} \cdot \frac{w}{z^{q^{2}} + w^{2}}} + 1}},$which takes into account the air flow through each perforated tile,which was calculated as described above. The Lorentzian field is chosento yield 0 at the center of the tile and converge to 1 at largedistances from the tile. By way of example only, as described inconjunction with the description of FIG. 14 below, the half point of theresponse function is at the tile edges. So at 2 to 3 tiles away (about 4feet to about 6 feet) the value of the Lorentzian field will be closeto 1. The width of the Lorentzian field can be a function of the airflow where larger flows could result in a slower convergence to 1 withdistance (wider fields, more impact). This process is repeated bymultiplying the Lorentzian fields at each tile location with theprevious fields. The process yields a 2D surface with very low values(close to 0) in the vicinity of tiles and higher values (close to 1) atlocations far away from the tiles. An exemplary response function matrixis shown in FIG. 14. A key shown to the right of the distribution inFIG. 14 shows the Lorentzian field values ranging from 0 to 1. Noteknowing the “pixel” translation w can be related to a distance with aunit. In this particular example, 1 tile=2 feet corresponds to 6 pixels.If w is set to 6 the half point of the response function is at thetiles' edges. It is also noted that other response functions can beapplied—possibly some of which reflect the shape of the tile (usually asquare shape).

An average temperature increase distribution in the data center is thencalculated, which is given by the difference between ceiling T_(c) andplenum temperature T_(p) distributions, which were determined in steps320 and 314, respectively, described above. This average temperatureincrease distribution is multiplied by the product of the Lorentzianfields and the plenum temperature distribution is added to it to yieldthe floor temperature distribution T_(f) as follows:

${T_{f}\left( {x,y} \right)} = {{{\left\lbrack {\prod\limits_{q}^{\#\mspace{14mu}{oftiles}}{{resp}^{q}\left( {x,y} \right)}} \right\rbrack \cdot \Delta}\;{T/2}} + {T_{p}\left( {x,y} \right)}}$with Δ T/2 = (T_(c)(x, y) − T_(p)(x, y))/2The process yields floor temperatures very near to the plenumtemperature at locations close to tiles and average temperatures atlocations far away from tiles.

An exemplary matrix of

$\prod\limits_{q}^{\#\mspace{14mu}{oftiles}}{{resp}^{q}\left( {x,y} \right)}$with w=10 (1.67 feet) is shown in FIG. 15A and an exemplary matrix of

$\prod\limits_{q}^{\#\mspace{14mu}{oftiles}}{{resp}^{q}\left( {x,y} \right)}$with w=5 (0.83 feet) is shown in FIG. 15B. A key shown to the right ofthe distribution in FIG. 15A shows values ranging from 0 to 1, and a keyshown to the right of the distribution in FIG. 15B shows values alsoranging from 0 to 1. As provided above, MMT cart data can be used to fitparameters such as 1) the width of the Lorentzian fields, 2) thetemperature increase across the rack inlet and exhaust and 3) a dampingparameter, with the goal being to optimize/fine-tune the process byfinding the parameters that give the best fit to the data obtained fromthe MMT cart. Thus, the values of the “pixel” translation w given aboveare merely exemplary and other values can be chosen to better fit theMMT cart data.

The floor temperature distribution T_(f) (see FIGS. 15A and 15B) isessentially an array (or grid) of regularly spaced data (pressure)points. The raised floor mask (created in step 310, described above) isthen applied to the floor temperature distribution array. Essentially,the mask tells if a point in the array/grid is occupied by a structureor equipment (in this case servers, furniture, etc.) or is free(unoccupied).

The corresponding resulting floor temperature distributions after the RFmask has been applied are shown in FIGS. 16A and 16B. Specifically, anexemplary floor temperature distribution with w=10 (1.67 feet) is shownin FIG. 16A and an exemplary floor temperature distribution with w=5(0.83 feet) is shown in FIG. 16B. A key shown to the right of thedistribution in FIG. 16A shows temperature values ranging from 56.6° F.to 67.4° F., and a key shown to the right of the distribution in FIG.16B shows temperature values ranging from 56.3° F. to 73.1661° F.

Finally, in step 330, from the ceiling and floor temperaturedistributions, a three dimensional temperature distribution for the(e.g., data center) room (also referred to herein as a raised floortemperature distribution) is obtained by interpolating between thesevalues using different approaches. One approach includes using ans-curve. S-curves are described, for example, in U.S. patent applicationSer. No. 12/540,213 filed by Hamann et al., entitled “Knowledge-BasedModels for Data Centers,” the contents of which are incorporated byreference herein. Alternatively, a simple linear interpolation betweenthe floor and the ceiling temperature may be employed. Linearinterpolation is a standard method known to those of skill in the artand thus is not described further herein.

Exemplary resulting raised floor temperature distributions are shown inFIGS. 17A and 17B. Specifically, an exemplary raised floor temperaturedistribution at 4.5 feet above the floor with ΔT=12° C. is shown in FIG.17A and an exemplary raised floor temperature distribution at 4.5 feetwith ΔT=4° C. is shown in FIG. 17B. Height is factored through thelinear interpolation or the s-curve interpolation. Basically, for agiven height the distribution is obtained by interpolating between thefloor temperature distribution and the ceiling temperature distribution.A key shown to the right of the distribution in FIG. 17A showstemperature values ranging from 65.6° F. to 82.4° F., and a key shown tothe right of the distribution in FIG. 17B shows temperature valuesranging from 67.2° F. to 78.9° F.

Turning now to FIG. 18, a block diagram is shown of an apparatus 1800for creating a three-dimensional temperature distribution model for aroom (such as data center 100) having a floor and a ceiling, inaccordance with one embodiment of the present invention. It should beunderstood that apparatus 1800 represents one embodiment forimplementing methodology 300 of FIG. 3, described above.

Apparatus 1800 includes a computer system 1810 and removable media 1850.Computer system 1810 includes a processor device 1820, a networkinterface 1825, a memory 1830, a media interface 1835 and an optionaldisplay 1840. Network interface 1825 allows computer system 1810 toconnect to a network, while media interface 1835 allows computer system1810 to interact with media, such as a hard drive or removable media1850.

As is known in the art, the methods and apparatus discussed herein maybe distributed as an article of manufacture that itself includes amachine-readable medium containing one or more programs which whenexecuted implement embodiments of the present invention. For instance,the machine-readable medium may contain a program configured todetermine a ceiling temperature distribution in the room; determine afloor temperature distribution in the room; and interpolate between theceiling temperature distribution and the floor temperature distributionto obtain the three-dimensional temperature distribution model for theroom.

The machine-readable medium may be a recordable medium (e.g., floppydisks, hard drive, optical disks such as removable media 1850, or memorycards) or may be a transmission medium (e.g., a network comprisingfiber-optics, the world-wide web, cables, or a wireless channel usingtime-division multiple access, code-division multiple access, or otherradio-frequency channel). Any medium known or developed that can storeinformation suitable for use with a computer system may be used.

Processor device 1820 can be configured to implement the methods, steps,and functions disclosed herein. The memory 1830 could be distributed orlocal and the processor device 1820 could be distributed or singular.The memory 1830 could be implemented as an electrical, magnetic oroptical memory, or any combination of these or other types of storagedevices. Moreover, the term “memory” should be construed broadly enoughto encompass any information able to be read from, or written to, anaddress in the addressable space accessed by processor device 1820. Withthis definition, information on a network, accessible through networkinterface 1825, is still within memory 1830 because the processor device1820 can retrieve the information from the network. It should be notedthat each distributed processor that makes up processor device 1820generally contains its own addressable memory space. It should also benoted that some or all of computer system 1810 can be incorporated intoan application-specific or general-use integrated circuit.

Optional video display 1840 is any type of video display suitable forinteracting with a human user of apparatus 1800. Generally, videodisplay 1840 is a computer monitor or other similar video display.

Although illustrative embodiments of the present invention have beendescribed herein, it is to be understood that the invention is notlimited to those precise embodiments, and that various other changes andmodifications may be made by one skilled in the art without departingfrom the scope of the invention.

What is claimed is:
 1. A method for creating a three-dimensionaltemperature distribution model for a room having a floor and a ceiling,the method comprising the steps of: determining an energy balance in theroom based on total heat input into the room and total heat extractedfrom the room; calculating a mean temperature proximal to the ceilingusing the energy balance to ensure that the mean temperature isconsistent with a heat load in the room; obtaining streaming real-timesensor data from a network of sensors located in the room, wherein thenetwork of sensors comprises real-time power sensors, real-time pressuresensors, real-time air flow sensors, and real-time thermal sensors;weighting the streaming real-time sensor data obtained from each of thereal-time thermal sensors by a distance of each of the real-time thermalsensors from the ceiling to account for the real-time thermal sensorsbeing at different heights in the room; determining a firsttwo-dimensional temperature distribution in the room proximal to theceiling using the streaming real-time sensor data from a first set ofthe network of sensors; scaling the first two-dimensional temperaturedistribution such that a mean of the first two-dimensional temperaturedistribution is equal to the mean temperature calculated using theenergy balance thereby preserving the energy balance between the heatload in the room and temperature measured using the network of sensors;determining a second two-dimensional temperature distribution in theroom proximal to the floor using the streaming real-time sensor datafrom a second set of the network of sensors different from the firstset; and interpolating between the first two-dimensional temperaturedistribution and the second two-dimensional temperature distribution toobtain the three-dimensional temperature distribution model for the roomwhich conforms to a principle of energy balance, wherein the room is adata center having a sub-floor plenum beneath the floor and wherein thethree-dimensional temperature distribution model is used to implementcooling within the data center in a manner that improves energyefficiency.
 2. The method of claim 1, wherein cooled air is provided tothe data center through the sub-floor plenum by way of perforated tilesin the floor.
 3. The method of claim 2, further comprising the step of:obtaining power consumption data from equipment in the data center. 4.The method of claim 3, wherein the power consumption data comprises datafrom power distribution units in the data center, the equipment in thedata center which receive power through the power distribution units andthe equipment in the data center which do not receive power through thepower distribution units.
 5. The method of claim 4, wherein theequipment in the data center which receive power through the powerdistribution units comprise lighting in the data center, airconditioning units in the data center and coolant distribution units inthe data center.
 6. The method of claim 5, wherein the air conditioningunits in the data center each comprise a blower motor to circulate airthrough the air conditioning unit and to blow cooled air into thesub-floor plenum, the method further comprising the step of: obtainingone or more of power data, blower setting data and air flow data forblower motors.
 7. The method of claim 5, wherein the data center furthercomprises a plurality of equipment racks, each of the equipment rackshaving an air inlet side and an air outlet side, the method furthercomprising the steps of: obtaining real-time inlet air temperature datafrom one or more of the air inlet sides of the equipment racks;obtaining real-time discharge air temperature data from one or more ofthe air conditioning units; obtaining real-time discharge air flow datafrom one or more of the air conditioning units; and obtaining real-timesub-floor plenum pressure data from the sub-floor plenum.
 8. The methodof claim 7, wherein the real-time inlet air temperature data from one ormore of the air inlet sides of the equipment racks and the real-timedischarge air temperature data from one or more of the air conditioningunits are obtained using the real-time thermal sensors.
 9. The method ofclaim 7, wherein the real-time discharge air flow data from one or moreof the air conditioning units is obtained using the real-time air flowsensors.
 10. The method of claim 7, wherein the real-time sub-floorplenum pressure data from the sub-floor plenum is obtained using thereal-time pressure sensors.
 11. The method of claim 7, furthercomprising the step of: obtaining real-time outlet air temperature datafrom one or more of the air outlet sides of the equipment racks usingvirtual sensors.
 12. The method of claim 7, wherein the real-time inletair temperature data from one or more of the air inlet sides of theequipment racks is used to determine the ceiling temperaturedistribution.
 13. The method of claim 7, further comprising the step of:calculating a sub-floor plenum pressure distribution based on an inverseweighted distance of the real-time sub-floor plenum pressure data fromthe sub-floor plenum; using the sub-floor plenum pressure distributionto determine air flow from each of the perforated tiles in the floor;and using the air flow from each of the perforated tiles in the floorand an average temperature increase distribution in the data center todetermine the floor temperature distribution.
 14. The method of claim13, further comprising the step of: applying a normalized Lorentzianfield to each of the perforated tiles in the floor.
 15. The method ofclaim 2, further comprising the step of: creating a convolution mask forthe sub-floor plenum which indicates what portions of the sub-floorplenum comprise open space and what portions of the sub-floor plenum areblocked off.
 16. The method of claim 15, further comprising the step of:obtaining real-time sub-floor plenum temperature data from the sub-floorplenum; using the real-time sub-floor plenum temperature data tocalculate a sub-floor plenum temperature distribution; and applying theconvolution mask for the sub-floor plenum to the sub-floor plenumtemperature distribution to determine a mean sub-floor plenumtemperature.
 17. The method of claim 16, wherein the sub-floor plenumtemperature distribution is calculated based on the inverse weighteddistance of the real-time sub-floor plenum temperature data.
 18. Themethod of claim 16, further comprising the step of: using the meansub-floor plenum temperature to determine a mean ceiling temperaturebased on a heat load in the data center and a total air flow in the datacenter attributable to the air conditioning units.
 19. The method ofclaim 1, further comprising the steps of: creating a convolution maskfor the room which indicates what portions of the room comprise openspace and what portions of the room are blocked off; and creating aconvolution mask for the ceiling which indicates what portions of theceiling comprise open space and what portions of the ceiling are blockedoff.
 20. An apparatus for creating a three-dimensional temperaturedistribution model for a room having a floor and a ceiling, theapparatus comprising: a memory; and at least one processor device,coupled to the memory, operative to: determine an energy balance in theroom based on total heat input into the room and total heat extractedfrom the room; calculate a mean temperature proximal to the ceilingusing the energy balance to ensure that the mean temperature isconsistent with a heat load in the room; obtain streaming real-timesensor data from a network of sensors located in the room, wherein thenetwork of sensors comprises real-time power sensors, real-time pressuresensors, real-time air flow sensors, and real-time thermal sensors;weight the streaming real-time sensor data obtained from each of thereal-time thermal sensors by a distance of each of the real-time thermalsensors from the ceiling to account for the real-time thermal sensorsbeing at different heights in the room; determine a firsttwo-dimensional temperature distribution in the room proximal to theceiling using the streaming real-time sensor data from a first set ofthe network of sensors; scale the first two-dimensional temperaturedistribution such that a mean of the first two-dimensional temperaturedistribution is equal to the mean temperature calculated using theenergy balance thereby preserving the energy balance between the heatload in the room and temperature measured using the network of sensors;determine a second two-dimensional temperature distribution in the roomproximal to the floor using the streaming real-time sensor data from asecond set of the network of sensors different from the first set; andinterpolate between the first two-dimensional temperature distributionand the second two-dimensional temperature distribution to obtain thethree-dimensional temperature distribution model for the room whichconforms to a principle of energy balance, wherein the room is a datacenter having a sub-floor plenum beneath the floor and wherein thethree-dimensional temperature distribution model is used to implementcooling within the data center in a manner that improves energyefficiency.
 21. The apparatus of claim 20, wherein cooled air isprovided to the data center through the sub-floor plenum by way ofperforated tiles in the floor.
 22. A non-transitory article ofmanufacture for creating a three-dimensional temperature distributionmodel for a room having a floor and a ceiling, comprising amachine-readable medium containing one or more programs which whenexecuted implement the steps of: determining an energy balance in theroom based on total heat input into the room and total heat extractedfrom the room; calculating a mean temperature proximal to the ceilingusing the energy balance to ensure that the mean temperature isconsistent with a heat load in the room; obtaining streaming real-timesensor data from a network of sensors located in the room, wherein thenetwork of sensors comprises real-time power sensors, real-time pressuresensors, real-time air flow sensors, and real-time thermal sensors;weighting the streaming real-time sensor data obtained from each of thereal-time thermal sensors by a distance of each of the real-time thermalsensors from the ceiling to account for the real-time thermal sensorsbeing at different heights in the room; determining a firsttwo-dimensional temperature distribution in the room proximal to theceiling using the streaming real-time sensor data from a first set ofthe network of sensors; scaling the first two-dimensional temperaturedistribution such that a mean of the first two-dimensional temperaturedistribution is equal to the mean temperature calculated using theenergy balance thereby preserving the energy balance between the heatload in the room and temperature measured using the network of sensors;determining a second two-dimensional temperature distribution in theroom proximal to the floor using the streaming real-time sensor datafrom a second set of the network of sensors different from the firstset; and interpolating between the first two-dimensional temperaturedistribution and the second two-dimensional temperature distribution toobtain the three-dimensional temperature distribution model for the roomwhich conforms to a principle of energy balance, wherein the room is adata center having a sub-floor plenum beneath the floor and wherein thethree-dimensional temperature distribution model is used to implementcooling within the data center in a manner that improves energyefficiency.
 23. The article of manufacture of claim 22, wherein cooledair is provided to the data center through the sub-floor plenum by wayof perforated tiles in the floor.